STOCHASTIC_GRADIENT_ND_NOISE
Optimal Control with Stochastic Noise

STOCHASTIC_GRADIENT_ND_NOISE is a MATLAB program which solves an optimal control problem involving a functional over a system with stochastic noise, by Jeff Borggaard, Catalin Trenchea, Clayton Webster.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

BLACK_SCHOLES, a MATLAB library which implements some simple approaches to the Black-Scholes option valuation theory;;

CNOISE, a MATLAB library which generates samples of noise obeying a 1/f^alpha power law, by Miroslav Stoyanov.

ONED, a MATLAB library which contains functions useful for 1D finite element calculations.

OPTIMAL_CONTROL_1D, a MATLAB program which seeks the optimal control function for a one dimensional system which is represented using the finite element formulation;

PCE_LEGENDRE, a MATLAB program which assembles the system matrix associated with a polynomal chaos expansion of a 2D stochastic PDE, using Legendre polynomials;

STOCHASTIC_DIFFUSION, MATLAB functions which implement several versions of a stochastic diffusivity coefficient.

Author:

Jeff Borggaard, Catalin Trenchea, Clayton Webster.

Source Code:

• exact_expected_value.m returns the exact expected value of the solution and the control.
• f_function.m RHS function from exact coefficient Q and the exact solution U.
• monte_carlo.m returns the physical coordinates of Monte Carlo abscissas.
• oned_bilinear.m integrates kernel(x) * basis function(x) * test function(x).
• oned_f_int.m computes the integral of f(x) times a test function.
• oned_gauss.m sets Gauss integration points on (-1,1).
• oned_mesh.m generates a mesh with a prescribed density. This routine returns elements of the same type as xb, e_connb (linear or quadratic)
• oned_shape.m computes test functions and derivatives for a Lagrange C0 element given element coordinates and Gauss points. (assumes all nodes are uniformly distributed in the element.)
• optimal_control.m is a script to solve the optimal control problem.
• q_exact.m evaluates the exact control coefficient function.
• u_hat.m is the exact target function to be matched.

Examples and Tests:

• optimal_control_adjoint_mc_driver.m driver for the 1D optimal control problem.
• optimal_control_adjoint_mc_driver_output.txt the output file.
• figure01.png output figure 1.
• figure02.png output figure 2.
• figure05.png output figure 5.
• figure06.png output figure 6.
• figure07.png output figure 7.
• figure08.png output figure 8.

You can go up one level to the MATLAB source codes.